Question

IT TAKES ROBERT 9 HRS.LONGRE TO CONSTRUCT A FENCE THAT ITR TAKES ELDRIN. IF THEY WORK TOGETHER THEY CAN CONSTRUCT THE FENCE IN 20 HRS. HOW LONG WOULD IT TAKE EACH WORKING ALONE TO CONSTRUCT A FENCE?

Answer 1

Why are you yelling?

Answer 2

I got 36 and 45 hours.

Answer 3

Let eldrin complete the work in x hrs
therefore robert completes it in x+9 hrs

Work done by eldrin in 1 hr = 1/x
Work done by robert in 1 hr= 1/x+9

Therefore work doen by elderin and robert together in a day =
(1/x) +(1/x+9)

By data work is done in 20 hrs, therefore
[ (1/x) + (1/x+9)]*20=1 (total work done amounts to 1)
Therefore simplifying we get =

(20/x) + (20/x+9)=1
20(x+9) + 20x/x(x+9)=1 (taking LCM)
20x + 180 + 20x / x^2 +9x = 1
40x +180=x^2 +9x (cross multiplication)
x^2 -31x -180 = 0
x^2 -36x +5x -180=0
x(x-36) +5 (x-36)=0
(x+5)(x-36)=0

Therefore x=36(Applicable) or x=-5(Not applicable)

Therefore eldrin takes 36 hrs and robert 45 hrs !!!

Please give a good answer!!!

Answer 4

this is how i also got 36 and 45

Answer 5

@alexray19: By solving \[ x (9 + x) - 20 (9 + 2 x) = 0 \] then then neglecting the negative solution.